Olympics - Hungary Has Double Digit Lead in Gold? (Population Relative) I created a Web page that pulls in live Olympic medal results from Thompson Reuters and worldwide population counts from the CIA.
The results are interesting to me - Hungary has a double digit lead in gold medals over the rest of the world.  Also, the USA and China are near the bottom in just about every category.
My question is - am I presenting the data in a fair manner?  I simply took the largest population then created a factor for each country based on that.  Relative medal count columns are based on that factor.
What column(s) could I add?  What other factors could I add to present the fairest view?  The absolute view is easy - Reuters does that.   How to create a fair view?
https://rack.pub/rio

 A: Smaller countries can get an advantage in two ways.

*

*Systematic advantage because the number of athletes per country is limited.
Large countries like the USA and China, who have populations 25 and 100 times larger than Hungary, are not sending an equivalent amount of athletes or teams. For instance, in many team sports there is only one team per country competing and in individual sports the number of entries per country is limited.


*Stochastic advantage because variations are larger for smaller countries.
The coefficient of variation for the number of medals will be smaller when the expected value is larger.
Example if every athlete rolls a six sided dice. Then the countries with the largest (but also the smallest) average dice roll will often be countries with a smaller amount of athletes. See the simulation below where we have hundred countries with 50 athletes and hundred countries with 200 athletes.

Idea for the image from vondj's YouTube video: Kleine Schulen sind besser! Lügen mit der gefährlichsten Formel der Welt

I imagine a graph of number of medals versus population might show some interesting insights. (There are several on the internet, but they are often for only a single year and with some noise, am average of several editions might give a good view of the relationship between medals and population)
A: You are trying to find an estimate of any individual's chance to win a medal, knowing that the "data" we have is just the number by country. It's a great question a fair solution being closer to the spirit of Olympics.
Basically, this is a statistical problem which is well approximated by your method as the average number (frequency) of medals (for each color) relative to the population. But how reliable is this method? This is pretty close to the problem of estimating the reliability of a binomial toss from different number of throws which has applications for instance to compare the quality of resellers in Amazon based on different feedback numbers (see this thorough explanation).
In this particular case, the population number is always enough to make the approximation of the beta distribution with a normal - such that it is certainly possible to compare the significativity of each estimate for each country. 
